Orthogonal graph layout algorithms aim to produce clear, compact, and readable network diagrams by arranging nodes and edges along horizontal and vertical lines, while minimizing bends and crossings. Most existing orthogonal layout methods focus primarily on quality criteria such as area usage, total edge length, and bend minimization. Explicitly controlling the global aspect ratio (AR) of the resulting layout is as of now unexplored. Existing orthogonal layout methods offer no control over the resulting AR and their rigid geometric constraints make adaptation of finished layouts difficult. With the increasing variety of aspect ratios encountered in daily life, from wide monitors to tall mobile devices or fixed-size interface panels, there is a clear need for aspect ratio control in orthogonal layout methods. To tackle this issue, we introduce Aspect Ratio-Constrained Orthogonal Layout (ARCOL). Building upon the Human-like Orthogonal Layout Algorithm (HOLA)~\cite{Kieffer2016}, we integrate aspect ratio at two different stages: (1) into the stress minimization phase, as a soft constraint, allowing the layout algorithm to gently guide node positions toward a specified target AR, while preserving visual clarity and topological faithfulness; and (2) into the tree reattachment phase, where we modify the cost function to favor placements that improve the AR. We evaluate our approach through quantitative evaluation and a user study, as well as expert interviews. Our evaluations show that ARCOL produces balanced and space efficient orthogonal layouts across diverse aspect ratios.

Detecting and interpreting common patterns in relational data is crucial for understanding complex topological structures across various domains. These patterns, or network motifs, can often be detected algorithmically. However, visual inspection remains vital for exploring and discovering patterns. This paper focuses on presenting motifs within BioFabric network visualizations-a unique technique that opens opportunities for research on scaling to larger networks, design variations, and layout algorithms to better expose motifs. Our goal is to show how highlighting motifs can assist users in identifying and interpreting patterns in BioFabric visualizations. To this end, we leverage existing motif simplification techniques. We replace edges with glyphs representing fundamental motifs such as staircases, cliques, paths, and connector nodes. The results of our controlled experiment and usage scenarios demonstrate that motif simplification for BioFabric is useful for detecting and interpreting network patterns. Our participants were faster and more confident using the simplified view without sacrificing accuracy. The efficacy of our current motif simplification approach depends on which extant layout algorithm is used. We hope our promising findings on user performance will motivate future research on layout algorithms tailored to maximizing motif presentation. Our supplemental material is available at https://osf.io/f8s3g/?view_only=7e2df9109dfd4e6c85b89ed828320843.

Storyline visualizations represent character interactions over time. When these characters belong to different groups, a new research question emerges: how can we balance optimization of readability across the groups while preserving the overall narrative structure of the story? Traditional algorithms that optimize global readability metrics (like minimizing crossings) can introduce quality biases between the different groups based on their cardinality and other aspects of the data. Visual consequences of these biases are: making characters of minority groups disproportionately harder to follow, and visually deprioritizing important characters when their curves become entangled with numerous secondary characters. We present F2Stories, a modular framework that addresses these challenges in storylines by offering three complementary optimization modes: (1) fairnessMode ensures that no group bears a disproportionate burden of visualization complexity regardless of their representation in the story; (2) focusMode allows prioritizing a group of characters while maintaining good readability for secondary characters; and (3) standardMode globally optimizes classical aesthetic metrics. Our approach is based on Mixed Integer Linear Programming (MILP), offering optimality guarantees, precise balancing of competing metrics through weighted objectives, and the flexibility to incorporate complex fairness concepts as additional constraints without the need to redesign the entire algorithm. We conducted an extensive experimental analysis to demonstrate how F2Stories enables more fair or focus group-prioritized storyline visualizations while maintaining adherence to established layout constraints. Our evaluation includes comprehensive results from a detailed case study that shows the effectiveness of our approach in real-world narrative contexts. An open access copy of this paper and all supplemental materials are available at osf.io/e2qvy.

This report describes the 32nd Annual Graph Drawing Contest, held in conjunction with the 33rd International Symposium on Graph Drawing and Network Visualization (GD'25) at Linköping University, Norrköping, Sweden. The mission of the Graph Drawing Contest is to monitor and challenge the current state of the art in graph-drawing technology. This year’s edition featured two categories, a creative topic in which participants visualized a dataset based on the Netflix show Dark and a live challenge held at the conference where participants had to draw a graph on a grid, such that the drawing is k-planar for as low a k as possible. A special feature of this year’s contest is that the submissions to the creative topic were exhibited in the "Norrköping Decision Arena", a room with a circular annulus-shaped screen.

Uncertainty is common to most types of data, from meteorology to the biomedical sciences. Here, we are interested in the visualization of uncertainty within the context of multivariate graphs, specifically the visualization of uncertainty attached to node attributes. Many visual channels offer themselves up for the visualization of node attributes and their uncertainty. One controversial and relatively under-explored channel, however, is animation, despite its conceptual advantages. In this paper, we investigate node “wiggliness”, i.e. uncertainty-dependent pseudo-random motion of nodes, as a potential new visual channel with which to communicate node attribute uncertainty. To study wiggliness’ effectiveness, we compare it against three other visual channels identified from a thorough review of uncertainty visualization literature—namely node enclosure, node fuzziness, and node color saturation. In a larger-scale, mixed method, Prolific -crowd-sourced, online user study of 160 participants, we quantitatively and qualitatively compare these four uncertainty encodings across eight low-level graph analysis tasks that probe participants’ abilities to parse the presented networks both on an attribute and topological level. We ultimately conclude that all four uncertainty encodings appear comparably useful—as opposed to previous findings. Wiggliness may be a suitable and effective visual channel with which to communicate node attribute uncertainty, at least for the kinds of data and tasks considered in our study.

Abstract Biofabric is a novel method for network visualization, with promising potential to highlight specific network features. Recent studies emphasize the importance of staircase motifs — equivalent to fans or stars in node‐link diagrams — within Biofabric. However, to effectively showcase these motifs, we need to formulate specialized layout algorithms. This paper introduces a method to compute optimal layouts for Biofabric, focusing on maximizing staircase formation. We present an Integer Linear Programming (ILP) model for this task and evaluate its performance in terms of scalability and output quality against a leading heuristic method, Degreecending. Our results demonstrate that the ILP approach identifies significantly more, and often longer, staircases compared to Degreecending, albeit with the trade‐off of higher computation times. Our supplemental material, including a full copy of the paper, code, and results, is available on osf.io.

Abstract Physicalizations, which combine perceptual and sensorimotor interactions, offer an immersive way to comprehend complex data visualizations by stimulating active construction and manipulation. This study investigates the impact of personal construction on the comprehension of physicalized networks. We propose a physicalization toolkit— NODKANT —for constructing modular node‐link diagrams consisting of a magnetic surface, 3D printable and stackable node labels, and edges of adjustable length. In a mixed‐methods between‐subject lab study with 27 participants, three groups of people used NODKANT to complete a series of low‐level analysis tasks in the context of an animal contact network. The first group was tasked with freely constructing their network using a sorted edge list, the second group received step‐by‐step instructions to create a predefined layout, and the third group received a pre‐constructed representation. While free construction proved on average more time‐consuming, we show that users extract more insights from the data during construction and interact with their representation more frequently, compared to those presented with step‐by‐step instructions. Interestingly, the increased time demand cannot be measured in users' subjective task load. Finally, our findings indicate that participants who constructed their own representations were able to recall more detailed insights after a period of 10–14 days compared to those who were given a pre‐constructed network physicalization. All materials, data, code for generating instructions, and 3D printable meshes are available on https://osf.io/tk3g5/ .

Visualizing relational data is crucial for understanding complex connections between entities in social networks, political affiliations, or biological interactions. Well-known representations like node-link diagrams and adjacency matrices offer valuable insights, but their effectiveness relies on the ability to identify patterns in the underlying topological structure. Reordering strategies and layout algorithms play a vital role in the visualization process since the arrangement of nodes, edges, or cells influences the visibility of these patterns. The BioFabric visualization combines elements of node-link diagrams and adjacency matrices, leveraging the strengths of both, the visual clarity of node-link diagrams and the tabular organization of adjacency matrices. A unique characteristic of BioFabric is the possibility to reorder nodes and edges separately. This raises the question of which combination of layout algorithms best reveals certain patterns. In this paper, we discuss patterns and anti-patterns in BioFabric, such as staircases or escalators, relate them to already established patterns, and propose metrics to evaluate their quality. Based on these quality metrics, we compared combinations of well-established reordering techniques applied to BioFabric with a well-known benchmark data set. Our experiments indicate that the edge order has a stronger influence on revealing patterns than the node layout. The results show that the best combination for revealing staircases is a barycentric node layout, together with an edge order based on node indices and length. Our research contributes a first building block for many promising future research directions, which we also share and discuss. A free copy of this paper and all supplemental materials are available at https://osf.io/9mt8r/?view_only=b7t0dfbe550e3404f83059afdc60184c6.

As Differential Privacy (DP) transitions from theory to practice, visualization has surfaced as a catalyst in promoting acceptance and usage. Despite the potential of visualization tools to support differential privacy implementation, their development is limited by a lack of understanding of the overall deployment process, practitioner challenges, and the role of visual tools in real-world deployments. To narrow this gap, we interviewed 18 professionals from various backgrounds who regularly engage with differential privacy in their work. Our objectives were to understand the differential privacy implementation process and associated challenges; explore the actors (individuals involved in differential privacy implementation), how they use or struggle to use visualization; and identify the benefits and challenges of using visualization in the implementation process. Our results delineate the differential privacy implementation process into five distinct stages and highlight the main actors alongside the diverse visualization applications and shortcomings. We find that visualizations can be used to build foundational differential privacy knowledge, describe implementation parameters, and evaluate private outputs. However, the visualization strategies described often fail to address the diverse technical backgrounds and varied privacy and accuracy concerns of users, hindering effective communication between the different actors involved in the implementation process. From our findings, we propose three research directions: visualizations for setting and evaluating noise addition, evaluation of uncertainty visualization related to trust in differential privacy, and research focused on pedagogical visualizations for complex data science topics.

A layered graph is an important category of graph in which every node is assigned to a layer, and layers are drawn as parallel or radial lines. They are commonly used to display temporal data or hierarchical graphs. Previous research has demonstrated that minimizing edge crossings is the most important criterion to consider when looking to improve the readability of such graphs. While heuristic approaches exist for crossing minimization, we are interested in optimal approaches to the problem that prioritize human readability over computational scalability. We aim to improve the usefulness and applicability of such optimal methods by understanding and improving their scalability to larger graphs. This paper categorizes and evaluates the state-of-the-art linear programming formulations for exact crossing minimization and describes nine new and existing techniques that could plausibly accelerate the optimization algorithm. Through a computational evaluation, we explore each technique's effect on calculation time and how the techniques assist or inhibit one another, allowing researchers and practitioners to adapt them to the characteristics of their graphs. Our best-performing techniques yielded a median improvement of 2.5-17 × depending on the solver used, giving us the capability to create optimal layouts faster and for larger graphs. We provide an open-source implementation of our methodology in Python, where users can pick which combination of techniques to enable according to their use case. A free copy of this paper and all supplemental materials, datasets used, and source code are available at https://osf.io/5vq79.

Abstract Evaluations—encompassing computational evaluations, benchmarks and user studies—are essential tools for validating the performance and applicability of graph and network layout algorithms (also known as graph drawing). These evaluations not only offer significant insights into an algorithm's performance and capabilities, but also assist the reader in determining if the algorithm is suitable for a specific purpose, such as handling graphs with a high volume of nodes or dense graphs. Unfortunately, there is no standard approach for evaluating layout algorithms. Prior work holds a ‘Wild West’ of diverse benchmark datasets and data characteristics, as well as varied evaluation metrics and ways to report results. It is often difficult to compare layout algorithms without first implementing them and then running your own evaluation. In this systematic review, we delve into the myriad of methodologies employed to conduct evaluations—the utilized techniques, reported outcomes and the pros and cons of choosing one approach over another. Our examination extends beyond computational evaluations, encompassing user‐centric evaluations, thus presenting a comprehensive understanding of algorithm validation. This systematic review—and its accompanying website—guides readers through evaluation types, the types of results reported, and the available benchmark datasets and their data characteristics. Our objective is to provide a valuable resource for readers to understand and effectively apply various evaluation methods for graph layout algorithms. A free copy of this paper and all supplemental material is available at osf.io , and the categorized papers are accessible on our website at https://visdunneright.github.io/gd‐comp‐eval/ .

Abstract The visual analysis of multivariate network data is a common yet difficult task in many domains. The major challenge is to visualize the network's topology and additional attributes for entities and their connections. Although node‐link diagrams and adjacency matrices are widespread, they have inherent limitations. Node‐link diagrams struggle to scale effectively, while adjacency matrices can fail to represent network topologies clearly. In this paper, we delve into the design space of BioFabric, which aligns entities along rows and relationships along columns, providing a way to encapsulate multiple attributes for both. We explore how we can leverage the unique opportunities offered by BioFabric's design space to visualize multivariate network data — focusing on three main categories: juxtaposed visualizations, embedded on‐node and on‐edge encoding, and transformed node and edge encoding. We complement our exploration with a quantitative assessment comparing BioFabric to adjacency matrices. We postulate that the expansive design possibilities introduced in BioFabric network visualization have the potential for the visualization of multivariate data, and we advocate for further evaluation of the associated design space. Our supplemental material is available on osf.io.

Immersive analytics has emerged as a promising research area, leveraging advances in immersive display technologies and techniques, such as virtual and augmented reality, to facilitate data exploration and decision-making. This paper presents a systematic literature review of 73 studies published between 2013-2022 on immersive analytics systems and visualizations, aiming to identify and categorize the primary dimensions influencing their design. We identified five key dimensions: Academic Theory and Contribution, Immersive Technology, Data, Spatial Presentation, and Visual Presentation. Academic Theory and Contribution assess the motivations behind the works and their theoretical frameworks. Immersive Technology examines the display and input modalities, while Data dimension focuses on dataset types and generation. Spatial Presentation discusses the environment, space, embodiment, and collaboration aspects in IA, and Visual Presentation explores the visual elements, facet and position, and manipulation of views. By examining each dimension individually and cross-referencing them, this review uncovers trends and relationships that help inform the design of immersive systems visualizations. This analysis provides valuable insights for researchers and practitioners, offering guidance in designing future immersive analytics systems and shaping the trajectory of this rapidly evolving field.

Generative text-to-image models (as exemplified by DALL-E, MidJourney, and Stable Diffusion) have recently made enormous technological leaps, demonstrating impressive results in many graphical domains-from logo design to digital painting to photographic composition. However, the quality of these results has led to existential crises in some fields of art, leading to questions about the role of human agency in the production of meaning in a graphical context. Such issues are central to visualization, and while these generative models have yet to be widely applied in visualization, it seems only a matter of time until their integration is manifest. Seeking to circumvent similar ponderous dilemmas, we attempt to understand the roles that generative models might play across visualization. We do so by constructing a framework that characterizes what these technologies offer at various stages of the visualization workflow, augmented and analyzed through semi-structured interviews with 21 experts from related domains. Through this work, we map the space of opportunities and risks that might arise in this intersection, identifying doomsday prophecies and delicious low-hanging fruits that are ripe for research.

Internet routing is largely dependent on Border Gateway Protocol (BGP). However, BGP does not have any inherent authentication or integrity mechanisms that help make it secure. Effective security is challenging or infeasible to implement due to high costs, policy employment in these distributed systems, and unique routing behavior. Visualization tools provide an attractive alternative in lieu of traditional security approaches. Several BGP security visualization tools have been developed as a stop-gap in the face of ever-present BGP attacks. Even though the target users, tasks, and domain remain largely consistent across such tools, many diverse visualization designs have been proposed. The purpose of this study is to provide an initial formalization of methods and visualization techniques for BGP cybersecurity analysis. Using PRISMA guidelines, we provide a systematic review and survey of 29 BGP visualization tools with their tasks, implementation techniques, and attacks and anomalies that they were intended for. We focused on BGP visualization tools as the main inclusion criteria to best capture the visualization techniques used in this domain while excluding solely algorithmic solutions and other detection tools that do not involve user interaction or interpretation. We take the unique approach of connecting (1) the actual BGP attacks and anomalies used to validate existing tools with (2) the techniques employed to detect them. In this way, we contribute an analysis of which techniques can be used for each attack type. Furthermore, we can see the evolution of visualization solutions in this domain as new attack types are discovered. This systematic review provides the groundwork for future designers and researchers building visualization tools for providing BGP cybersecurity, including an understanding of the state-of-the-art in this space and an analysis of what techniques are appropriate for each attack type. Our novel security visualization survey methodology-connecting visualization techniques with appropriate attack types-may also assist future researchers conducting systematic reviews of security visualizations. All supplemental materials are available at https://osf.io/tupz6/.

Abstract Hypergraphs are a generalization of graphs in which edges (hyperedges) can connect more than two vertices—as opposed to ordinary graphs where edges involve only two vertices. Hypergraphs are a fairly common data structure but there is little consensus on how to visualize them. To optimize a hypergraph drawing for readability, we need a layout algorithm. Common graph layout algorithms only consider ordinary graphs and do not take hyperedges into account. We focus on layered hypergraphs, a particular class of hypergraphs that, like layered graphs, assigns every vertex to a layer, and the vertices in a layer are drawn aligned on a linear axis with the axes arranged in parallel. In this paper, we propose a general method to apply layered graph layout algorithms to layered hypergraphs. We introduce six different transformations for layered hypergraphs. The choice of transformation affects the subsequent graph layout algorithm in terms of computational performance and readability of the results. Thus, we perform a comparative evaluation of these transformations in terms of number of crossings, edge length, and impact on performance. We also provide two case studies showing how our transformations can be applied to real‐life use cases. A copy of this paper with all appendices and supplemental material is available at osf.io/grvwu.

Node-link visualizations are a familiar and powerful tool for displaying the relationships in a network. The readability of these visualizations highly depends on the spatial layout used for the nodes. In this paper, we focus on computing layered layouts, in which nodes are aligned on a set of parallel axes to better expose hierarchical or sequential relationships. Heuristic-based layouts are widely used as they scale well to larger networks and usually create readable, albeit sub-optimal, visualizations. We instead use a layout optimization model that prioritizes optimality - as compared to scalability - because an optimal solution not only represents the best attainable result, but can also serve as a baseline to evaluate the effectiveness of layout heuristics. We take an important step towards powerful and flexible network visualization by proposing Stratisfimal Layout, a modular integer-linear-programming formulation that can consider several important readability criteria simultaneously - crossing reduction, edge bendiness, and nested and multi-layer groups. The layout can be adapted to diverse use cases through its modularity. Individual features can be enabled and customized depending on the application. We provide open-source and documented implementations of the layout, both for web-based and desktop visualizations. As a proof-of-concept, we apply it to the problem of visualizing complicated SQL queries, which have features that we believe cannot be addressed by existing layout optimization models. We also include a benchmark network generator and the results of an empirical evaluation to assess the performance trade-offs of our design choices. A full version of this paper with all appendices, data, and source code is available at osf.io/qdyt9 with live examples at https://visdunneright.github.io/stratisfimal/.

Virtual reality (VR) researchers struggle to conduct remote studies. Previous work has focused on working around limitations imposed by traditional crowdsourcing methods. However, the potential for leveraging social VR platforms for HCI evaluations is largely unexplored. These platforms have large VR-ready user populations, distributed synchronous virtual environments, and support for user-generated content. We demonstrate how social VR platforms can be used to practically and ethically produce valid research results by replicating two studies using one such platform (VRChat): a quantitative study on Fitts’ Law and a qualitative study on tabletop collaboration. Our replication studies exhibited analogous results to the originals, indicating the research validity of this approach. Moreover, we easily recruited experienced VR users with their own hardware for synchronous, remote, and collaborative participation. We further provide lessons learned for future researchers experimenting using social VR platforms. This paper and all supplemental materials are available at osf.io/c2amz.

Temporal event sequence alignment has been used in many domains to visualize nuanced changes and interactions over time. Existing approaches align one or two sentinel events. Overview tasks require examining all alignments of interest using interaction and time or juxtaposition of many visualizations. Furthermore, any event attribute overviews are not closely tied to sequence visualizations. We present Sequence Braiding, a novel overview visualization for temporal event sequences and attributes using a layered directed acyclic network. Sequence Braiding visually aligns many temporal events and attribute groups simultaneously and supports arbitrary ordering, absence, and duplication of events. In a controlled experiment we compare Sequence Braiding and IDMVis on user task completion time, correctness, error, and confidence. Our results provide good evidence that users of Sequence Braiding can understand high-level patterns and trends faster and with similar error. A full version of this paper with all appendices; the evaluation stimuli, data, and analysis code; and source code are available at [Formula: see text].

Timelines are commonly represented on a horizontal line, which is not necessarily the most effective way to visualize temporal event sequences. However, few experiments have evaluated how timeline shape influences task performance. We present the design and results of a controlled experiment run on Amazon Mechanical Turk (n=192) in which we evaluate how timeline shape affects task completion time, correctness, and user preference. We tested 12 combinations of 4 shapes --- horizontal line, vertical line, circle, and spiral — and 3 data types — recurrent, non-recurrent, and mixed event sequences. We found good evidence that timeline shape meaningfully affects user task completion time but not correctness and that users have a strong shape preference. Building on our results, we present design guidelines for creating effective timeline visualizations based on user task and data types. A free copy of this paper, the evaluation stimuli and data, and code are available https://osf.io/qr5yu/